Merge pull request #76 from tapumar/patch-1

Create LCS.py

string/LCS.py

@@ -0,0 +1,26 @@
+def lcs(a, b):
+    lengths = [[0 for j in range(len(b)+1)] for i in range(len(a)+1)]
+
+    # row 0 and column 0 are initialized to 0 already
+
+    for i, x in enumerate(a):
+        for j, y in enumerate(b):
+            if x == y:
+                lengths[i+1][j+1] = lengths[i][j] + 1
+            else:
+                lengths[i+1][j+1] = max(lengths[i+1][j], lengths[i][j+1])
+
+    # read the substring out from the matrix
+    result = ""
+    x, y = len(a), len(b)
+    while x != 0 and y != 0:
+        if lengths[x][y] == lengths[x-1][y]:
+            x -= 1
+        elif lengths[x][y] == lengths[x][y-1]:
+            y -= 1
+        else:
+            assert a[x-1] == b[y-1]
+            result = a[x-1] + result
+            x -= 1
+            y -= 1
+    return result